Relationships between frequentist and theoretical probability through a random experiment simulation from the theory of didactic situations. (Innovaciones Educativas, 2025)
This research aims to characterize how students relate frequentist probability to theoretical probability in a didactic situation that uses a simulator of random experiments. The Theory of Didactic Situations (Brousseau, 2007) was chosen for both the design and the construction and analysis of a class. The methodology consists of a qualitative approach that analyzes the results according to the phases of the Theory of Didactic Situations, identifying the arguments established by students based on different probabilistic meanings. The classroom proposal was implemented in a seventh-grade basic education class at a private school located in the city of Valparaíso, Chile. The activity was divided into five parts, from a recreational instance posed through initial bets about what is in a bag with tokens,  to the institutionalization of the law of large numbers. The results showed that most working pairs, when addressing the problem, based their strategies primarily on intuitive and frequentist approaches; however, some students validated their results using arguments associated with both frequentist and theoretical approaches to probability. In relation to this, one of the conclusions is that the frequentist results obtained were validated using the theoretical approach.
Keywords: Probability; Teaching method; Basic education; Teaching materials